Using origami folding concepts to design novel mechanical metamaterials has recently become a prevalent framework. Inspired by the Kresling origami structure, this study proposes a double-layer Kresling origami metamaterial with reprogrammable shock stiffness. Two combination strategies are constructed, each with different geometric constraints and kinematic compatibility. They are identified as assigned with same torsion direction (ASTD) and assigned with opposite torsion direction (AOTD), respectively. The shock stiffness of two double-layer Kresling origami metamaterials is analyzed using the finite element method, and results indicate that the AOTD metamaterial has superior impact resistance. Furthermore, the programmability of shock stiffness of the metamaterial is carried out comprehensively, and the influence of each design parameter is exhibited in detail. Finally, two prototypes of ASTD and AOTD metamaterials are fabricated, and experimental tests verify the analysis outcomes. This study provides a new approach to constructing mechanical metamaterials with reprogrammable shock stiffness for applications in energy absorption and vibration isolation engineering.